Anuradha Gupta, Manu Rohilla
The influence of errors on the convergence of infinite products of weak quasi-contraction mappings in $b$-metric spaces is explored. An example demonstrating the necessity of convergence of the sequence of computational errors to zero is also provided. Moreover, we discuss weak ergodic theorems in the setting of $b$-metric spaces.
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In this paper, we introduce the concept of monotone Gregus-Ćirić-contraction mappings in weighted digraphs. Then we establish a fixed point theorem for monotone Gregus-Ćirić-contraction mappings defined in convex weighted digraphs.
We study the convergence analysis of a Picard-S iteration method for a particular class of weak-contraction mappings. Furthermore, we prove a data dependence result for fixed point of the class of weak-contraction mappings with the help of the Picard-S iteration methods.
Cyclic p-$ϕ$-contraction mappings
本文提出循环p-φ压缩映射的概念，并研究其在不同空间中的固定点存在性和唯一性。
Fixed Point Theorems for TSR-Contraction Mapping in Probabilistic Metric Spaces
本文在概率度量空间中引入TSR-压缩原理，证明满足该原理的函数存在唯一不动点，区别于传统压缩映射定义。
In this paper, we introduce the new generalization of contraction mapping by a new control function and an altering distance . We establish some existence results of fixed point for such mappings. Our results reproduce several old and new results in the literature.
Best Proximity Point Results for Cyclic Orbital Contraction Mappings in $CAT_p(0)$ Metric Spaces
本文在CAT_p(0)度量空间中研究了循环轨道收缩映射的最佳接近点存在性，并探讨了其在一致凸巴拿赫空间中的应用。
Let (X, d) be a complete metric space, and let S, T : X to CB(X) be a duality of multi-valued generalized weak contraction mappings or a duality of generalized weak contraction mappings. We discuss the common fixed points and endpoints of the two kinds of multi-valued weak mappings. Our results extend and improve some results given by Daffer and Kaneko (1995), Rouhani and Moradi (2010), and Moradi and Khojasteh (2011).
The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Zamfirescu and T-weak contraction mappings in the framework of complete cone metric spaces.
Coupled best proximity point theorems for $p$-cyclic $ϕ$-contraction and $p$-cyclic Kannan nonexpansive mappings
本文提出两类新的循环映射概念，并证明其耦合最佳逼近点的存在性。
We consider the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of strict contractions is a σ-porous subset.
Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Θ$- contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $Θ$-contraction mappings are obtained. An example is presented to support the results presented herein. An application t…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
Petrov type extension for multivalued contraction mappings
本文引入了三角形λ%-收缩周长的概念，扩展了Nadler收缩，分析了多值映射的连续性及与经典多值收缩的关系，并通过反例说明多值λ-收缩周长映射不一定是多值λ-收缩。同时引入了构成三角形的性质，并探讨其与多值映射无周期为2的周期点的关系，最后给出了多值映射的固定点结果。
We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Kransnoselskij iterative scheme. Several important results in fixed point theory are shown to be corollaries or consequences of the main results in this paper. We also study the fixed points of local enriched contractions, asymptotic enriched contractions and Maia type…
Another Perspective on Chatterjea Contraction
本文从Chatterjea收缩映射的角度出发，探讨了在保持映射自身不等式左边的情况下，该结论的成立条件，并在k-连续性的假设下，证明了新的收缩映射类m-Chatterjea收缩映射在完备度量空间中存在唯一不动点，并通过例子验证了该类严格包含Chatterjea映射类。
We introduce a large class of contractive mappings, called Suzuki Berinde type contraction. We show that any Suzuki Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mapping is also obtained. These results unify, generalize and complement various known comparable results in the literature.
Convergence of C-Class Enriched Hardy-Rogers Contractions in some Banach Spaces
本文利用C类函数推广富集Hardy-Rogers压缩映射，在Banach空间中通过迭代格式建立唯一不动点及公共不动点的收敛性，推广了近期相关结果。
A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is proven that if the space is uniformly convex and the subsets are non-empty, closed and convex then all the iterations converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduce to a unique fixed point if all such subsets intersect.
Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions an…
In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point property of the average operator of the mappings. Further, we study the well-posedness and limit shadowing property of the fixed point problem involving the contractions, and give some examples to validate the results proved. We frame an open question related to the existence of a fixed point of such contractions. We also show that Berinde and Păcurar's rec…
Fixed Point Theory For Singh-Chatterjea Type Contractive Mappings
本文提出结合Singh扩展与Chatterjea压缩的Singh-Chatterjea压缩条件，在完备度量空间中建立映射第p次迭代的不动点定理，推广并统一了经典结果，并通过示例与数值实现验证其适用性。
We consider a relatively new hybrid generalized F-contraction involving a pair of mappings and utilize the same to prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings satisfying generalized $(F,φ)$-contraction condition under common limit range property in complete metric spaces. A similar result involving a hybrid pair of mappings satisfying a Rational type Hardy-Rogers $(F,φ)$-contractive condition is also proved. Our results generalize and improve several results of the existing literature. As applications of our results, we prove two theo…
We show that iterative scheme due to Karahan and Özdemir (2013) can be used to approximate fixed point of contraction mappings. Furthermore, we prove that CR iterative scheme converges faster than the iterative scheme due to Karahan and Özdemir (2013) for the class contraction mappings. Finally, we prove a data dependence result for contraction mappings by employing iterative scheme due to Karahan and Özdemir (2013).
A new contraction principle on the perimeters of triangles and related results
本文提出了一种在完备度量空间中收缩三角形周长的新映射，并通过固定点定理研究空间的度量完备性。
In this note, at first we prove that the existence of best proximity points for cyclic relatively nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic relatively nonexpansive mappings in the setting of strictly convex Banach spaces by using the projection operator. In this way, we conclude that a main result of the paper "Proximal normal structure and relatively nonexpansive mappings", Studia Math., (171~(2005) 283--293) immediately follows. We then discuss the convergence of best proximity pairs for noncyclic contractions by applying the convergence of it…
In this paper, we give a generalization of Hicks type contractions and Golet type contractions on fuzzy metric spaces. We prove some fixed point theorems for this new type contractions mappings on fuzzy metric spaces.
Fixed Point Theorems for Paired Contractive Mappings in $b$-Metric Spaces
本文在b-度量空间中引入配对-Chatterjea压缩概念，建立相关不动点定理，证明其恰当扩展Chatterjea型压缩，还研究配对及配对-Kannan压缩的不动点结果，通过例子说明结果适用性，扩展推广了现有不动点定理。
Some Fixed Point Results for Interpolative Contractive Mappings in $C^{\ast}$-algebra valued metric spaces
该研究在$C^{\text{*}}$-代数值完备度量空间框架下提出插值压缩映射新概念，证明了Kannan-Riech型压缩映射的不动点及公共不动点的存在性，拓展了相关不动点理论范畴。
This paper is devoted to prove the S. L. Singh's common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of Generalized Kannan Con- traction, Generalized Zamfirescu Contraction and Generalized Weak Contraction for a pair of mappings, proving afterward their respective fixed point results.
On the weakest conditions for the existence of fixed points of Kannan and Chatterjea type contractions
本文研究Kannan和Chatterjea型收缩映射固定点存在的最弱条件，扩展了Suzuki的方法，证明所提条件最优且确保Picard序列收敛。
We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we show that the typical nonexpansive mapping is a Rakotch contraction on every bounded subset and that there is a bounded set which is mapped into itself by this mapping. In particular, we obtain that the typical nonexpansive mapping in this setting has a unique fixed point which can be reached by iterating the mapping. Nevertheless, it turns out that the typical mapping is not a Rakotch contraction on the whole space an…
On Significant Pointwise Contractions and Annular Contractions
本文引入显著逐点压缩和环形压缩两类映射，推广了Banach压缩，证明了在完备度量空间中显著逐点压缩存在不动点且可通过Picard迭代逼近，并在紧度量空间中证明了显著逐点收缩的不动点存在性。
Path--Averaged Contractions: A New Generalization of the Banach Contraction Principle
该研究提出新型自映射PA-压缩（路径平均压缩），证明完备度量空间上连续PA-压缩有唯一不动点且Picard迭代收敛，严格推广Banach压缩原理，验证其与多种经典压缩映射独立，可捕捉逐点压缩失效时的长期压缩行为。
On the Picard-Lindelöf Argument and the Banach-Caccioppoli Contraction Mapping Principle
本文通过改进收缩映射原理，实现了对皮卡-林德勒夫定理中收敛速率的精确恢复。
Our aim in this paper is to present a new type of the modular space. This space contains the classical modular space. There are some mappings that do not have contractive condition in the usual modular space but become contraction in this new space.
A Study of Kirk's Asymptotic Contractions via Leader Contractions
本文研究非线性压缩的渐近不动点结果，通过证明渐近Kirk压缩是Leader压缩消除有界轨道假设，弱化控制函数phi的连续性条件，统一并推广了多个基础结果，简化了不动点论证。
In this paper, by using admissible sets, we give some fixed point results for orbitally contractions which diminish the radius of invariant convex subsets and orbits. Furthermore, a characterization of the weak normal structure by the fixed point property associated with this class of mappings is established.
We show that the typical nonexpansive mapping on a small enough subset of a CAT($κ$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $σ$-porous set and therefore also of the first Baire category. Moreover, we exhibit metric spaces where strict contractions are not dense in the space of nonexpansive mappings. In some of these cases we show that all continuous self-mappings have a fixed point nevertheless.
We introduce a new iteration method called Picard-S iteration. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and converges faster than CR iteration method for the aforementioned class of mappings. Furthermore, by providing an example, it is shown that the Picard-S iteration method converges faster than all Picard, Mann, Ishikawa, Noor, SP, CR, S and some other iteration methods in the existing literature when applied to contraction mappings. A data dependence result is proven …
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction mappings.The second result deals with the fixed point of the strict contraction mappings where the modular satisfies the delta-condition. For the nonexpansive mappings,where the modular satisfies the regular growth condition,we present a fixed point theorem of the Shauder's type,without boundedness condition on the domain of theses mappings.
In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that the new iteration method is equivalent to both Mann iteration method and Picard-Mann hybrid iteration method and also converges faster than Picard-Mann hybrid iteration method for the class of almost contraction mappings. In addition to these we give a table and graphics for support this result. Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method.
In this article, we investigate for some sufficient conditions for the existence and uniqueness of best proximity points for the topological $p$-proximal contractions and $p$-proximal contractive mappings on arbitrary topological spaces. Moreover, our results are authenticated by a few numerical examples and these generalize some of the known results in the literature.
On The Existence of \(P\)-Contractions that are not Enriched Contractions
该论文通过构造两个不同类型的P-压缩映射实例，否定回答了2024年Altun等人提出的关于富集P-压缩映射与富集压缩映射关系的问题。
Fixed sets and fixed points in $\Lim$--spaces]{Fixed sets and fixed points for mappings in generalized $\Lim$--spaces of Fréchet
本文在公理化定义的广义Fréchet $\Lim$--空间中，借助偏序集值类距离函数研究压缩映射，并建立了Ćirić型和Caristi型广义压缩的不动集与不动点定理。
Some Fixed Point Theorems in $(α,β)$- Metric Spaces with applications to Fredholm integral and non-linear differential equations
本文提出$(α,β)$-度量空间及两类压缩映射，建立不动点定理并推广现有结果，证明Kannan和Reich定理，最后应用于Fredholm积分方程和非线性微分方程。
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(κ)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $σ$-porous subset. For separable metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical points of its domain. These results contain the case of nonexpansive self-mappings and the case of nonexpansive set-…
In this paper we propose a new iteration process, called the K iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes like Picard-S iteration process, Thakur New iteration process and Vatan Twostep iteration process for contraction mappings. We support our analytic proof by a numerical example. Stability of K iteration process and data dependence result for contraction mappings by employing K iteration process is also discussed. Finally we prove some weak and strong convergence theorems for the Suzuki gen…
In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results applies, in particular, to the study of solvability of functional equations arising in dynamic programming.
Generalized Proinov-type contractions using simulation functions with applications to fractals
本文通过模拟函数推广Proinov型压缩映射，提出Proinov型Z-压缩，证明其在拟度量空间中不动点的存在唯一性，并构建对应迭代函数系统，证明其存在唯一吸引子。
In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contraction mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also, we establish the existence of solution of strong accretive operator equation in linear 2-normed spaces.
Let $H$ be an infinite dimensional, reflexive, separable Hilbert space and $NA(H)$ the class of all norm-attainble operators on $H.$ In this note, we study an implicit scheme for a canonical representation of nonexpansive contractions in norm-attainable classes.
Fixed Points of Asymptotic Pointwise Contractions under Local Uniform Convergence
本文研究了渐近点态收缩在局部一致收敛下的不动点问题，通过引入Boyd-Wong型条件，证明了连续映射在完备度量空间中具有有界轨道时，其迭代收敛于唯一不动点，扩展了Kirk的渐近收缩定理。
Fixed Point Theorems for Multivalued Weak Contractions in Cone Metric Spaces
本文研究了锥度量空间中多值弱压缩的不动点问题，将Berinde弱压缩原理推广至多值设定，利用正规锥结构证明了广义不动点定理，并提供了迭代逼近格式及在微分包含与变分不等式中的应用。
In this paper, we establish some common fixed point results for a new class of pair of contractions mappings having functions as contractive parameters, and satisfying certain commutative properties.
Study of Existence and Stability of Fixed Points of Hypotenuse Contracting Mappings with Applications to Parabolic PDE
本文在度量空间中引入斜边压缩映射，建立其不动点存在性与唯一性及Ulam-Hyers稳定性的充分条件，经几何分析区分其与其他压缩映射，最终将结果应用于非齐次线性抛物型PDE解的存在性证明。
Fixed Point Theorems for Relaxed Asymptotic Contractions via Two Quasi-Metrics
本文引入了新的渐近压缩类，通过两个直接由基础映射定义的拟度量，结合局部一致收敛到Boyd-Wong函数的边界函数序列，放宽了Kirk定理的假设并严格包含其为特殊情况，证明了在完备度量空间中连续映射的不动点存在性与唯一性及迭代收敛性。
Fixed Point Theorem for Path-Averaged Contractions in Complete b-Metric Spaces
本文在完备b-度量空间中证明了路径平均压缩的唯一不动点定理，并展示了其在扩展其他压缩原理中的应用。
In this paper, we prove a mean ergodic theorem for nonexpansive mappings in Hadamard (nonpositive curvature metric) spaces, which extends the Baillon nonlinear ergodic theorem. The main result shows that the sequence given by the Karcher means of iterations of a nonexpansive mapping with a nonempty fixed point set converges weakly to a fixed point of the mapping. This result also remains true for a 1-parameter continuous semigroup of contractions.
Fixed Point Theory Analysis of a Lambda Policy Iteration with Randomization for the Ćirić Contraction Operator
本文利用不动点理论分析针对弱压缩映射（如 Ćirić 压缩）的带随机化 Lambda 策略迭代，给出无限维策略空间中依概率 1 收敛的充分条件。
For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive Banach space and if there is $x^* \in J(x)$ such that $|\langle T(t) \, x,J(x)\rangle| \to 1 $ as $t \to \infty$, then there is a unit vector $y\in X$ which is an eigenvector of the generator $A$ of $(T_t)_{t>0}$ associated with a purely imaginary eigenvalue. They asked whether this result is still true if $X$ is replaced by $c_o$. In this article, we show th…
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